Coupling effects in dynamic calorimetry: Frequency-dependent relations for specific heat and thermomechanical responses — A one-dimensional approach based on thermodynamics with internal state variables

Lion, Alexander; Peters, J.

doi:10.1016/j.tca.2009.12.014

Cited by 17 publications

(25 citation statements)

References 33 publications

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“…The constitutive theory to be developed is a substantial extension of recently published approaches to model the glass transition of amorphous polymers, cf. [49][50][51][52] and [53].…”

Section: Fundamentalsmentioning

confidence: 99%

“…In order to represent the glass transition, the approach developed in [49] is applied. For further information, the reader is also referred to [51,52] and [53]. To this end, a quadratic dependence of the chemical potential on δ and two coupling terms with respect to pressure and temperature are introduced in combination with additional material parameters w, d, e and integration constants s 000 and μ 000 :…”

Section: Specific Gibbs Free Energymentioning

confidence: 99%

“…describing the temperature dependence of the internal variable δ, the WLF-equation is applied (cf. [50,53] or [55]). For the temperature-dependent factor of the function β (.…”

Section: Non-equilibrium Behaviourmentioning

confidence: 99%

“…In order to compute the specific heat, the derivatives appearing in (17) are computed under the assumption of p = 0. Taking (62) in combination with (49), (53) and (57) into account, the following expression is calculated at first:…”

Section: Non-equilibrium Behaviourmentioning

confidence: 99%

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A thermodynamic approach to model the caloric properties of semicrystalline polymers

Lion

Johlitz

2015

Continuum Mech. Thermodyn.

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It is well known that the crystallisation and melting behaviour of semicrystalline polymers depends in a pronounced manner on the temperature history. If the polymer is in the liquid state above the melting point, and the temperature is reduced to a level below the glass transition, the final degree of crystallinity, the amount of the rigid amorphous phase and the configurational state of the mobile amorphous phase strongly depend on the cooling rate. If the temperature is increased afterwards, the extents of cold crystallisation and melting are functions of the heating rate. Since crystalline and amorphous phases exhibit different densities, the specific volume depends also on the temperature history. In this article, a thermodynamically based phenomenological approach is developed which allows for the constitutive representation of these phenomena in the time domain. The degree of crystallinity and the configuration of the amorphous phase are represented by two internal state variables whose evolution equations are formulated under consideration of the second law of thermodynamics. The model for the specific Gibbs free energy takes the chemical potentials of the different phases and the mixture entropy into account. For simplification, it is assumed that the amount of the rigid amorphous phase is proportional to the degree of crystallinity. An essential outcome of the model is an equation in closed form for the equilibrium degree of crystallinity in dependence on pressure and temperature. Numerical simulations demonstrate that the process dependences of crystallisation and melting under consideration of the glass transition are represented.

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“…The constitutive theory to be developed is a substantial extension of recently published approaches to model the glass transition of amorphous polymers, cf. [49][50][51][52] and [53].…”

Section: Fundamentalsmentioning

confidence: 99%

Section: Specific Gibbs Free Energymentioning

confidence: 99%

“…describing the temperature dependence of the internal variable δ, the WLF-equation is applied (cf. [50,53] or [55]). For the temperature-dependent factor of the function β (.…”

Section: Non-equilibrium Behaviourmentioning

confidence: 99%

Section: Non-equilibrium Behaviourmentioning

confidence: 99%

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A thermodynamic approach to model the caloric properties of semicrystalline polymers

Lion

Johlitz

2015

Continuum Mech. Thermodyn.

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“…Classically, rubber-like elasticity is described as an entropic effect [17], which leads to heat production (absorption) during loading (unloading). The first experimental observations of this effect in the literature were those obtained by Gough 1 [18] and Joule [19], and dealt with the increase in temperature of rubber during stretching.…”

mentioning

confidence: 99%

Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading

Balandraud

Cam

2014

Arch Appl Mech

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. Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading. Archive of Applied Mechanics, Springer Verlag, 2014Verlag, , 84 (6), pp.773-788. 10.1007 Noname manuscript No. Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading the date of receipt and acceptance should be inserted later Abstract The present paper deals with the specificities of the thermal response of rubber under cyclic mechanical loading at constant ambient temperature. This question is important, since the stabilized thermal response is used in fatigue life criteria, especially for the fast evaluation of fatigue life. For this purpose, entropic coupling in a thermo-hyperelastic framework is first used to predict the variation in the heat source produced or absorbed by the material during cyclic loading. The heat diffusion equation is then used to deduce temperature variations under adiabatic and non-adiabatic conditions. The influence of several parameters on the stabilized thermal response is studied: signal shape, frequency, minimum and maximum stretch levels, multiaxiality of the mechanical state. The results show that, in the steady-state regime, the mean value between the maximum and minimum temperature variations over a mechanical cycle is different from zero. This is due to the specific variation in the heat source, which depends on both the stretch rate and the stretch level. This result has numerous consequences, in particular for fatigue. Indeed, the stabilized mean value between the maximum and minimum temperature variations during fatigue tests does not reflect only fatigue damage, since the entropic coupling also leads to a value different from zero. This is a major difference with respect to materials exhibiting only isentropic coupling, such as metallic materials.

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On a model of viscoelasticity with internal state variables

Peters

Estorff

Achenbach

et al. 2010

Proc Appl Math and Mech

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In classical theories of viscoelasticity, time-dependent effects are accounted for only with respect to the mechanical properties. However, glass-forming materials such as polymers, for example, also show viscoelastic effects in their thermal properties as can be seen from measurements of the coefficient of thermal expansion or the heat capacity. In this contribution, a model is presented that is able to describe effects associated with the glass transition in the mechanical as well as the thermal properties in one consistent approach. To this end, the state space known from equilibrium thermodynamics is enlarged by internal state variables. These variables are to describe the deviation from equilibrium, hence allowing for a description of viscoelastic effects. Closed form expressions for the complex modulus as well as the compliance, the complex heat capacity at constant stress as well as at constant strain, and the complex coefficient of thermal expansion as well as the thermal modulus are derived and discussed.

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Coupling effects in dynamic calorimetry: Frequency-dependent relations for specific heat and thermomechanical responses — A one-dimensional approach based on thermodynamics with internal state variables

Cited by 17 publications

References 33 publications

A thermodynamic approach to model the caloric properties of semicrystalline polymers

A thermodynamic approach to model the caloric properties of semicrystalline polymers

Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading

On a model of viscoelasticity with internal state variables

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